Stained vs. Polished concrete?

I am refinishing the floor of the lower level of our 1960 split level home. It is on a slab, and we have removed all flooring down to the slab. We would like to have the concrete remain as the flooring, and are planning to have it either polished or stained - and dyed in both cases.

I would like to know if one might look better in a residential setting, or if this is purely individual opinion?

My understanding is the that in polishing, they use increasingly fine grit grinders, up to 1500 or 3000 grit, then seal.

In staining, the grinding stops at about 50 or 100 grit, and then they use acrylic or wax, with a number of layers of wax. The result is less shiny/industrial, and maybe more rustic - but requires a little more upkeep.

I would appreciate any insights or experiences anyone may have. Thank you!